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Journal of Dynamical and Control Systems

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11-07-2016

When a Minimal Map Is Totally Transitive on a G-Space

Authors: Mukta Garg, Ruchi Das

Published in: Journal of Dynamical and Control Systems | Issue 3/2017

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Abstract

In this paper, we introduce the notion of G-regular periodic decomposition (GRPD) for maps on G-spaces and investigate its relation with G-transitivity. It is shown that if a pseudoequivariant, G-transitive map on a G-space has a GRPD of some length n, then its nth iterate is not G-transitive. On the other hand, if a pseudoequivariant, G-transitive map on a G-space has a non-G-transitive nth iterate, then it admits a GRPD of length p for some prime p dividing n. Using the notion of GRPD, it is obtained that a pseudoequivariant, G-minimal map is totally G-transitive on a connected G-space.

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Title: When a Minimal Map Is Totally Transitive on a G-Space
Authors: Mukta Garg
Ruchi Das
Publication date: 11-07-2016
Publisher: Springer US
Published in: Journal of Dynamical and Control Systems / Issue 3/2017
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-016-9336-5

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